Colloquium: The physics of axion stars

The particle that makes up the dark matter of the Universe could be an axion or axionlike particle. A collection of axions can condense into a bound Bose-Einstein condensate called an axion star. It is possible that a significant fraction of the axion dark matter is in the form of axion stars. This would make some efforts to identify the axion as the dark matter particle more challenging, but it would also open up new possibilities. The basic properties of axion stars, which can be gravitationally bound or bound by self-interactions, are summarized. Axions are naturally described by a relativistic field theory with a real scalar field, but low-energy axions can be described more simply by a classical nonrelativistic effective field theory with a complex scalar field.

Figure 1

Axion potential $V$ as a function of $\varphi$: chiral potential for $z=0.48$ (thick solid curve) and for $z=0.45$ and 0.51 (higher and lower thin solid curves) and instanton potential (dotted curve).

Figure 2

The tree-level diagrams for low-energy $3\to 3$ scattering in the relativistic axion theory. The first two diagrams are also diagrams in NREFT. In the third diagram, the thicker line indicates a virtual axion whose invariant mass is approximately $3m$.

Figure 3

Naive effective potential $V_{\mathrm{eff}}^{(0)}$ with $(1/2)m_a{\psi }^{*}\psi$ added as a function of $|\psi |$: chiral potentials for $z=0.48$ (thicker solid curve) and for $z=0.45$ and 0.51 (thinner solid curves) and instanton potential (dotted curve). The thin horizontal lines are the asymptotic values at large $|\psi |$.

Figure 4

Radius $R_{99}$ vs the mass $M=N{m}_a$ for the oscillon of the axion field. The axion mass is $m_a={10}^{-4}\mathrm{eV}$. The axion potential is either the chiral potential with $z=0.48$ (black lines) or the instanton potential (gray lines). The solid dot is the critical point that separates the unstable branch (dashed line) from the locally stable branch (solid line). The open dot marks the point to the left of which the lower branch is unstable to large fluctuations. The arrow indicates the direction of time evolution of the oscillon from the emission of relativistic waves.

Figure 5

Radius $R_{99}$ vs mass $M$ for a dilute axion star. The axion mass is $m_a={10}^{-4}\mathrm{eV}$. The axion potential is the chiral potential with $z=0.48$ (black lines) or the instanton potential (gray lines). The dot is a critical point that separates the stable branch (solid line) from the unstable branch (dashed line). The dotted line is for a boson star with no self-interactions. The arrow indicates the direction of time evolution of the axion star from the condensation of additional axions.

Figure 6

Contributions to the energy density $\rho (r)$ in the critical dilute axion star as functions of the radial coordinate $r$. Their absolute values are shown on a log scale, with positive (negative) contributions shown as solid (dashed) curves. The axion potential is the chiral potential with $z=0.48$ and $m_a={10}^{-4}\mathrm{eV}$. The curves in order of decreasing size at small $r$ are mass (black, multiplied by ${10}^{-14}$), gravitational (gray), potential (blue), and kinetic (red).

Figure 7

Contributions to the total energy of the stable dilute axion star as functions of its mass $M$. Their absolute values are shown on a log scale, with positive (negative) contributions shown as solid (dashed) curves. The curves in order of decreasing size are mass (black, multiplied by ${10}^{-14}$), gravitational (gray), kinetic (red), and potential (blue).

Figure 8

Radius $R_{99}$ vs mass $M$ for an axion star. The axion potential is the chiral potential with $z=0.48$ and $m_a={10}^{-4}\mathrm{eV}$. The dots are critical points that separate the stable branches (solid lines) from the unstable branch (dashed line). The dotted line is the Thomas-Fermi approximation.

Figure 9

Contributions to the energy density $\rho (r)$ in the critical dense axion star as functions of the radial coordinate $r$. Their absolute values are shown on a log scale, with positive (negative) contributions shown as solid (dashed) curves. The curves in order of decreasing size at $r=0.4R_{99*}$ are mass (black), kinetic (red), potential (blue), relativistic correction to kinetic (orange), and gravitational (gray, multiplied by $10^{10}$).

Figure 10

Contributions to the total energy of the locally stable dense axion star as functions of its mass $M=N{m}_a$. Their absolute values are shown on a log scale, with positive (negative) contributions shown as solid (dashed) curves. The curves in order of decreasing size at $M=3M_{*}$ are mass (black), potential (blue), kinetic (red), relativistic correction to kinetic (orange), and gravitational (gray, multiplied by $10^{12}$).